Measurement and Unit Conversions

69 questions

Question 21Question →

A coffee shop prepares cold brew coffee in large batches. Each batch produces exactly 33 gallons and 22 quarts of cold brew. The shop needs to completely fill three 44-gallon dispensers and two 22-gallon dispensers. If the shop has already prepared 704704 fluid ounces of cold brew, how many additional full batches must they prepare today to have enough cold brew to exactly fill all the dispensers?

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Answer: 3

Answer

3 batches
The correct answer is found by establishing a common unit of measurement, such as quarts. The total dispenser capacity is 16 gallons, which equals 64 quarts. The existing 704 fluid ounces is converted to 22 quarts (since there are 32 fluid ounces in a quart). Subtracting the 22 existing quarts from the 64 required quarts leaves 42 quarts needed. Finally, since one batch produces exactly 14 quarts (3 gallons + 2 quarts), we divide the 42 quarts needed by 14 quarts per batch to determine that 3 batches are required.

Step-by-Step Solution

1
Calculate the total required volume in gallons.
16 gallons
To find out the total capacity of the three 4-gallon dispensers and two 2-gallon dispensers.
2
Convert the total required volume from gallons to quarts.
64 quarts
Using a smaller common unit (quarts) makes it easier to subtract the existing fluid ounces and divide by the batch size.
3
Convert the already prepared cold brew from fluid ounces to quarts.
22 quarts
There are 32 fluid ounces in 1 quart. Dividing 704 by 32 gives the amount in quarts so it can be subtracted from the total.
4
Determine the remaining volume of cold brew needed.
42 quarts
Subtracting the existing volume (22 quarts) from the total required volume (64 quarts) gives the amount that still needs to be prepared.
5
Convert the volume of one batch to quarts.
14 quarts
One batch is 3 gallons (12 quarts) plus 2 quarts, which equals 14 quarts. This gives the unit rate per batch.
6
Calculate the number of additional batches needed.
3
Dividing the remaining needed volume (42 quarts) by the volume per batch (14 quarts) yields the exact number of batches required.

Key Concept

Converting and performing multi-step operations with US Customary units of capacity (gallons, quarts, and fluid ounces).
Estimated Time:2m 30s
Question 22Question →

An electrician needs to organize four pieces of copper wire. Arrange the following wire lengths in order from shortest to longest.

Drag items to arrange them in the correct order

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Answer

The correct order from shortest to longest is: 50 inches, 4 feet 6 inches, 5 feet, and 2 yards.
By converting all measurements to inches, we can clearly see the relative lengths: 50 inches is the shortest, followed by 4 feet 6 inches (which is 54 inches), then 5 feet (which is 60 inches), and finally 2 yards (which is 72 inches) as the longest.

Step-by-Step Solution

1
Identify the goal: convert all measurements to a single common unit to make comparison easy.
The target unit chosen is inches.
Comparing different units directly without conversion leads to errors.
2
Evaluate the first length: 50 inches.
50 inches remains 50 inches.
It is already in the target unit.
3
Convert the second length: 4 feet 6 inches into inches.
4×12=484 \times 12 = 48 inches. Adding the extra 6 inches gives 48+6=5448 + 6 = 54 inches.
There are 12 inches in 1 foot.
4
Convert the third length: 5 feet into inches.
5×12=605 \times 12 = 60 inches.
There are 12 inches in 1 foot.
5
Convert the fourth length: 2 yards into inches.
2×36=722 \times 36 = 72 inches.
There are 36 inches in 1 yard (or 3 feet per yard, and 12 inches per foot: 2×3×12=722 \times 3 \times 12 = 72).
6
Order the converted values from shortest to longest.
50 inches < 54 inches < 60 inches < 72 inches.
This confirms the final proper sequence of the wire pieces.

Key Concept

Converting between inches, feet, and yards to compare linear measurements.
Question 23Question →

A landscaper places two lengths of wooden garden edging end-to-end to border a flower bed. The first piece is 7127 \frac{1}{2} feet long, and the second piece is 4124 \frac{1}{2} feet long. What is the total length of the edging in inches?

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Answer: 144

Answer

144
First, the two fractional lengths must be combined: 7127 \frac{1}{2} plus 4124 \frac{1}{2} equals exactly 12 feet. Since there are 12 inches in a single foot, the total measurement in inches is found by multiplying the 12 feet by 12. This yields a final answer of 144 inches.

Step-by-Step Solution

1
Add the lengths of the two pieces of edging together in feet.
712+412=127 \frac{1}{2} + 4 \frac{1}{2} = 12 feet
Finding the total combined length is the first step before converting to the requested unit.
2
Convert the total length from feet to inches.
12×12=14412 \times 12 = 144 inches
There are 12 inches in 1 foot, so multiplying the number of feet by 12 gives the length in inches.

Key Concept

To convert US customary linear measurements from feet to inches, add the fractional lengths to find the total, then multiply the number of feet by 12.
Estimated Time:45s
Question 24Question →

A disaster relief organization is setting up a rectangular emergency water reservoir that measures 44 yards long, 33 yards wide, and 22 yards deep. The reservoir is currently filled to 75%75\% of its total capacity. If 11 cubic foot holds exactly 7.57.5 gallons of water, and the water is distributed into standard 33-gallon jugs, how many full jugs can be filled?

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Answer: 1,215

Answer

1,215
The correct answer is found by first calculating the volume in cubic yards (2424), converting it to cubic feet by multiplying by 2727 (648648), taking 75%75\% of that volume (486486), converting to total gallons by multiplying by 7.57.5 (3,6453,645), and finally dividing by 33 to find the number of jugs (1,2151,215).

Step-by-Step Solution

1
Calculate the total volume of the reservoir in cubic yards.
4×3×2=24 yd34 \times 3 \times 2 = 24 \text{ yd}^3
Multiplying the given length, width, and depth provides the total capacity of the rectangular reservoir.
2
Convert the volume from cubic yards to cubic feet.
24×27=648 ft324 \times 27 = 648 \text{ ft}^3
There are 3 feet in a yard, so there are 333^3, or 2727, cubic feet in one cubic yard.
3
Calculate the volume of water currently inside the reservoir.
648×0.75=486 ft3648 \times 0.75 = 486 \text{ ft}^3
The reservoir is filled to 75%75\% capacity, so we multiply the total volume by 0.750.75.
4
Convert the volume of the water into gallons.
486×7.5=3,645 gallons486 \times 7.5 = 3,645 \text{ gallons}
Each cubic foot holds 7.57.5 gallons, so multiplying by this rate gives the total gallons of water available.
5
Determine the number of full 33-gallon jugs that can be filled.
3,645÷3=1,215 jugs3,645 \div 3 = 1,215 \text{ jugs}
Dividing the total gallons of water by the capacity of a single jug gives the number of jugs.

Key Concept

Converting between linear dimensions and capacity, and applying multi-step rate calculations to find unit counts.
Question 25Question →

A heavy construction excavator is operated in two active shifts each day. The morning shift runs for 1.41.4 hours, and the afternoon shift runs for 2.82.8 hours. Between the shifts, the machine is turned off for a 4545-minute maintenance period. What is the total active operating time accumulated by the excavator over a 44-day project, in minutes?

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Answer: 1,0081,008

Answer

The total active operating time is 1,0081,008 minutes.
To find the total active time, first add the daily shift lengths: 1.41.4 hours + 2.82.8 hours = 4.24.2 hours per day. Multiply this by 44 days to get a total of 16.816.8 hours. Finally, convert the hours to minutes by multiplying by 6060, yielding 16.8×60=1,00816.8 \times 60 = 1,008 minutes.

Step-by-Step Solution

1
Calculate the total active operating hours per day.
1.4+2.8=4.21.4 + 2.8 = 4.2 hours.
Add the durations of the morning and afternoon shifts. The 4545-minute maintenance period is excluded because the question asks only for active operating time.
2
Calculate the total operating hours over the entire project.
4.2×4=16.84.2 \times 4 = 16.8 hours.
Multiply the daily operating time by the 44 days of the project to find the overall duration in hours.
3
Convert the total project hours into minutes.
16.8×60=1,00816.8 \times 60 = 1,008 minutes.
Multiply by 6060 to convert the hours into minutes, satisfying the unit requested in the question.

Key Concept

Converting decimal hours to minutes by multiplying by 60, and differentiating between active and inactive periods.
Question 26Question →

A warehouse worker is stacking identical shipping boxes. Each box is exactly 1616 inches tall. If the worker creates a single stack of 33 boxes, what is the total height of the stack in feet?

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Answer: 4

Answer

4 feet
The total height of the stack in inches is found by multiplying 1616 inches by 33, yielding 4848 inches. Because there are 1212 inches in 11 foot, dividing 4848 by 1212 gives the correct measurement of 44 feet.

Step-by-Step Solution

1
Calculate the total height in inches.
16×3=4816 \times 3 = 48 inches
To find the combined height of all 3 boxes before converting units.
2
Convert the total height from inches to feet.
48÷12=448 \div 12 = 4 feet
The question asks for the final height in feet, and there are 12 inches in a foot.

Key Concept

Converting US customary linear measurements (inches to feet).
Question 27Question →

A logistics officer is preparing a cargo flight and needs to balance the weight distribution of four different shipping pallets. Arrange the following pallets in order from the LIGHTEST to the HEAVIEST total mass.

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Answer

The correct order from lightest to heaviest is: Pallet 4, Pallet 1, Pallet 3, and Pallet 2.
By converting all measurements to kilograms, we find that Pallet 4 is 125 kg, Pallet 1 is 127.5 kg, Pallet 3 is 128 kg, and Pallet 2 is 135 kg. Ordering these mathematical products from lightest to heaviest yields Pallet 4, Pallet 1, Pallet 3, then Pallet 2.

Step-by-Step Solution

1
Select a common metric base unit for direct comparison.
Kilograms (kg) is chosen as the standard unit.
Comparing multiple quantities with different metric prefixes requires standardizing the units to avoid magnitude errors.
2
Calculate the total mass of Pallet 1.
150×0.85 kg=127.5 kg150 \times 0.85 \text{ kg} = 127.5 \text{ kg}.
Convert 850 g850 \text{ g} to kg by dividing by 1,0001,000, resulting in 0.85 kg0.85 \text{ kg} per kit. Multiply by the 150150 kits.
3
Calculate the total mass of Pallet 2.
45×3 kg=135 kg45 \times 3 \text{ kg} = 135 \text{ kg}.
Convert 3,000,000 mg3,000,000 \text{ mg} to kg by dividing by 1,000,0001,000,000 (since 1 kg=1,000,000 mg1 \text{ kg} = 1,000,000 \text{ mg}), resulting in 3 kg3 \text{ kg} per generator. Multiply by the 4545 generators.
4
Calculate the total mass of Pallet 3.
132 kg−4 kg=128 kg132 \text{ kg} - 4 \text{ kg} = 128 \text{ kg}.
Find the initial mass (60×2.2 kg=132 kg60 \times 2.2 \text{ kg} = 132 \text{ kg}). Convert the removed packaging to kg (4,000 g÷1,000=4 kg4,000 \text{ g} \div 1,000 = 4 \text{ kg}), and subtract it from the total.
5
Calculate the total mass of Pallet 4.
250×0.5 kg=125 kg250 \times 0.5 \text{ kg} = 125 \text{ kg}.
Convert 50,000 cg50,000 \text{ cg} to kg by dividing by 100,000100,000 (since 1 kg=100,000 cg1 \text{ kg} = 100,000 \text{ cg}), resulting in 0.5 kg0.5 \text{ kg} per filter. Multiply by the 250250 filters.
6
Order the final mass values from least to greatest.
Pallet 4 (125 kg125 \text{ kg}) < Pallet 1 (127.5 kg127.5 \text{ kg}) < Pallet 3 (128 kg128 \text{ kg}) < Pallet 2 (135 kg135 \text{ kg}).
The question asks for the arrangement from lightest to heaviest.

Key Concept

Metric Unit Conversions and Multi-Step Operations
Estimated Time:3m 0s
Question 28Question →

A Coast Guard coordinator is reviewing the maximum patrol durations of four different rescue vessels. Arrange the vessels' maximum patrol durations from longest to shortest.

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Answer

The correct sequence from longest to shortest is Vessel Protector, Vessel Sentinel, Vessel Guardian, and Vessel Defender.
Converting each vessel's duration to minutes reveals their true lengths: Vessel Protector is 148148 minutes, Vessel Sentinel is 145145 minutes (120+25120 + 25), Vessel Guardian is 144144 minutes (2.4×602.4 \times 60), and Vessel Defender is 142142 minutes (8,520÷608,520 \div 60). Ordering these numerical values from greatest to least produces the correct sequence.

Step-by-Step Solution

1
Identify the need to standardize all durations into a common unit.
Minutes are chosen as the standard unit.
Converting all times into minutes makes direct numerical comparison straightforward.
2
Convert Vessel Sentinel's duration to minutes.
145145 minutes
22 hours ×60=120\times 60 = 120 minutes. Adding the remaining 2525 minutes yields 145145 minutes.
3
Convert Vessel Guardian's duration to minutes.
144144 minutes
Multiply decimal hours by 6060. 2.4×60=1442.4 \times 60 = 144 minutes.
4
Convert Vessel Defender's duration to minutes.
142142 minutes
Divide seconds by 6060. 8,520÷60=1428,520 \div 60 = 142 minutes.
5
Compare all standardized times and arrange them from longest to shortest.
Protector (148148) > Sentinel (145145) > Guardian (144144) > Defender (142142)
To fulfill the core requirement of the prompt.

Key Concept

Converting mixed time units, decimal hours, and seconds into a common base unit to accurately compare elapsed durations.
Question 29Question →

A military supply truck has a fuel tank capacity of 45 gallons45 \text{ gallons}. The truck operates with a fuel efficiency of 8 kilometers per liter8 \text{ kilometers per liter}. Assuming the truck starts with a full tank of fuel, what is its maximum driving range in miles? (Use 1 gallon=3.8 liters1 \text{ gallon} = 3.8 \text{ liters} and 1 mile=1.6 kilometers1 \text{ mile} = 1.6 \text{ kilometers})

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Answer: 855

Answer

855
To find the range in miles, first convert the tank capacity to liters by multiplying 45 gallons by 3.8 liters/gallon to get 171 liters. Then, find the range in kilometers by multiplying 171 liters by 8 kilometers/liter, which equals 1,368 kilometers. Finally, convert the distance from kilometers to miles by dividing 1,368 by 1.6, resulting in exactly 855 miles.

Step-by-Step Solution

1
Convert the fuel tank capacity from gallons to liters.
45 gallons×3.8 liters/gallon=171 liters45 \text{ gallons} \times 3.8 \text{ liters/gallon} = 171 \text{ liters}
The fuel efficiency is given in kilometers per liter, so the total fuel volume must be in liters to find the total distance.
2
Calculate the maximum driving range in kilometers.
171 liters×8 km/liter=1,368 kilometers171 \text{ liters} \times 8 \text{ km/liter} = 1,368 \text{ kilometers}
Multiplying the total volume of fuel by the fuel efficiency yields the total distance the truck can travel in kilometers.
3
Convert the maximum driving range from kilometers to miles.
1,368 kilometers÷1.6 km/mile=855 miles1,368 \text{ kilometers} \div 1.6 \text{ km/mile} = 855 \text{ miles}
The question asks for the final distance in miles, requiring division by the conversion factor.

Key Concept

Inter-System Unit Conversions with Compound Rates
Question 30Question →

A post office charges a flat rate of $3.00\$ 3.00 per pound to ship a certain class of package. If a customer mails a package that weighs exactly 4848 ounces, what is the total shipping cost?

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Answer: $9.00\$ 9.00

Answer

$9.00\$ 9.00
To find the total shipping cost, first convert the given weight from ounces to pounds. Because there are 1616 ounces in 11 pound, you divide 4848 by 1616 to get 33 pounds. Next, multiply the weight in pounds by the shipping rate of $3.00\$ 3.00 per pound (3×3.00=9.003 \times 3.00 = 9.00). The correct total cost is $9.00\$ 9.00.

Step-by-Step Solution

1
Convert the weight of the package from ounces to pounds.
48 ounces÷16 ounces/pound=3 pounds48 \text{ ounces} \div 16 \text{ ounces/pound} = 3 \text{ pounds}
The shipping rate is given per pound, so the package weight must be calculated in pounds.
2
Calculate the total shipping cost by multiplying the weight in pounds by the rate per pound.
3 pounds×$3.00/pound=$9.003 \text{ pounds} \times \$ 3.00/\text{pound} = \$ 9.00
Total cost equals the unit rate multiplied by the total number of units.

Key Concept

US Customary Weight Measurements
Question 31Question →

A quartermaster is preparing individual equipment packs for a field training exercise. Arrange the following items in order from lightest to heaviest.

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Answer

The correct sequence from lightest to heaviest is: Radio battery, Utility knife, Medical kit, Entrenching tool.
To accurately compare the items, all weights must be in the same unit. Converting pounds to ounces (where 11 pound = 1616 ounces) reveals the actual weights: the Radio battery is 1010 oz, the Utility knife is 1616 oz, the Medical kit is 2020 oz, and the Entrenching tool is 3232 oz. Placing them in ascending order gives the correct arrangement.

Step-by-Step Solution

1
Identify the goal and the units provided in the problem.
The goal is to order the items from lowest weight to highest weight. The weights are given in a mix of ounces and pounds.
Before comparing values, all measurements must be converted to the same unit to ensure an accurate comparison.
2
Convert the weight of each item into ounces.
Radio battery = 1010 ounces. Utility knife = 11 pound = 1616 ounces. Medical kit = 2020 ounces. Entrenching tool = 22 pounds = 3232 ounces.
Using the standard conversion that 11 pound equals 1616 ounces makes it easy to compare all items using the smaller unit.
3
Sort the converted values from smallest to largest.
1010 ounces < 1616 ounces < 2020 ounces < 3232 ounces.
Sorting the unified measurements directly yields the final ordered list from lightest to heaviest.

Key Concept

To compare standard US customary weights, convert all measurements to the same unit using the conversion factor of 1616 ounces per pound.
Question 32Question →

A maintenance crew is scheduled to overhaul a radar system. The procedure consists of three sequential phases: diagnostics taking 11 hour and 4545 minutes, component replacement taking 22 hours and 3030 minutes, and recalibration taking 5555 minutes. If the crew begins the overhaul at 09200920 hours, at what time will the entire procedure be completed?

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Answer: 14301430 hours

Answer

The entire procedure will be completed at 14301430 hours.
The total duration of the three phases is 310 minutes, which converts to exactly 5 hours and 10 minutes. When you add this elapsed time to the starting clock time of 0920 hours, the final completion time correctly evaluates to 1430 hours.

Step-by-Step Solution

1
Convert the duration of all three phases into minutes to standardize the units.
Phase 1: 1 hour 45 minutes = 105 minutes. Phase 2: 2 hours 30 minutes = 150 minutes. Phase 3: 55 minutes.
Converting all times to a single unit prevents base-60 addition errors across mixed units.
2
Calculate the total duration of the overhaul by summing the minutes.
105 + 150 + 55 = 310 minutes.
The total time required is the sum of all individual phases.
3
Convert the total duration back into hours and minutes.
310 minutes divided by 60 equals 5 hours with a remainder of 10 minutes (5 hours and 10 minutes).
You must express the total elapsed time in hours and minutes to add it directly to a clock time.
4
Add the total duration to the starting time of 0920 hours.
0920 + 5 hours = 1420 hours; 1420 hours + 10 minutes = 1430 hours.
Adding the elapsed time to the initial clock time determines the final completion time.

Key Concept

Calculating total elapsed time by converting between minutes and hours (using a base-60 system) and applying it to a 24-hour military clock.

Alternative Method

Instead of converting to minutes, you can group the hours and minutes separately: Add the whole hours (1 hour + 2 hours = 3 hours). Then add the minutes (45 + 30 + 55 = 130 minutes). Convert the 130 minutes to 2 hours and 10 minutes, and combine this with the 3 hours to get a total duration of 5 hours and 10 minutes.
Estimated Time:1m 30s
Question 33Question →

A military field kitchen uses 128128 fluid ounces of vegetable oil to fry a batch of potatoes. How many quarts of vegetable oil does the kitchen use?

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Answer: 4

Answer

The kitchen uses 4 quarts of vegetable oil.
The correct answer accurately uses the conversion that 11 quart is equal to 3232 fluid ounces. By dividing the total 128128 fluid ounces by 3232, it correctly determines the volume is 44 quarts.

Step-by-Step Solution

1
Identify the proper conversion factor between fluid ounces and quarts.
1 quart is equal to 32 fluid ounces.
Converting a smaller capacity unit to a larger one requires knowing how many smaller units fit into one larger unit.
2
Divide the total fluid ounces by the number of fluid ounces in a quart.
128÷32=4128 \div 32 = 4
Since a quart is larger than a fluid ounce, division is required to find the equivalent amount in quarts.

Key Concept

Converting smaller units of US customary capacity to larger units using division.
Question 34Question →

A structural blueprint for a new commercial warehouse uses a scale of 12 inch=15 feet\frac{1}{2}\text{ inch} = 15\text{ feet}. On the blueprint, the rectangular main storage floor measures 313 inches3\frac{1}{3}\text{ inches} in length and 215 inches2\frac{1}{5}\text{ inches} in width. What is the actual area of the main storage floor in square feet?

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Answer: 6600

Answer

The actual area of the main storage floor is 6600 square feet.
To find the actual area, we first establish the true scale of the blueprint. Since 12 inch\frac{1}{2}\text{ inch} represents 15 feet15\text{ feet}, 1 inch1\text{ inch} represents 30 feet30\text{ feet}. The blueprint dimensions are given as mixed fractions: 313 inches3\frac{1}{3}\text{ inches} and 215 inches2\frac{1}{5}\text{ inches}. We convert these to the improper fractions 103\frac{10}{3} and 115\frac{11}{5}, and multiply each by the scale factor of 3030 to find the actual dimensions. The actual length is 103×30=100 feet\frac{10}{3} \times 30 = 100\text{ feet}, and the actual width is 115×30=66 feet\frac{11}{5} \times 30 = 66\text{ feet}. Finally, the area of the rectangle is found by multiplying the actual length by the actual width, yielding 100×66=6600 square feet100 \times 66 = 6600\text{ square feet}.

Step-by-Step Solution

1
Determine the unit scale rate.
1 inch=30 feet1\text{ inch} = 30\text{ feet}
The scale is given as 12 inch=15 feet\frac{1}{2}\text{ inch} = 15\text{ feet}. Multiplying both sides by 22 provides the actual distance per single inch on the drawing.
2
Calculate the actual length of the storage floor.
100 feet100\text{ feet}
Convert 3133\frac{1}{3} to the improper fraction 103\frac{10}{3}, then multiply by the scale factor of 3030: 103×30=100\frac{10}{3} \times 30 = 100.
3
Calculate the actual width of the storage floor.
66 feet66\text{ feet}
Convert 2152\frac{1}{5} to the improper fraction 115\frac{11}{5}, then multiply by the scale factor of 3030: 115×30=66\frac{11}{5} \times 30 = 66.
4
Calculate the actual area of the rectangular floor.
6600 square feet6600\text{ square feet}
Area is found by multiplying the actual length by the actual width: 100×66=6600100 \times 66 = 6600.

Key Concept

Scale Drawings and Map Measurements
Question 35Question →

A maintenance crew purchases 88 gallons of epoxy paint for a warehouse floor. They need to pour the paint into smaller trays that each hold exactly 22 quarts. How many trays can they fill completely?

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Answer: 16

Answer

16 trays
First, find the total number of quarts available. Because there are 4 quarts in 1 gallon, 8 gallons is equal to 32 quarts. Next, divide the 32 total quarts by the 2-quart capacity of each tray. This yields exactly 16 filled trays.

Step-by-Step Solution

1
Convert the total paint volume from gallons to quarts.
32 quarts
The trays are measured in quarts, so the total paint volume must be converted to the same unit. (8 gallons × 4 quarts/gallon = 32 quarts)
2
Divide the total number of quarts by the capacity of a single tray.
16 trays
This determines how many 2-quart portions can be distributed from the 32 quarts of paint. (32 quarts ÷ 2 quarts/tray = 16 trays)

Key Concept

Converting between standard US customary volume units (gallons to quarts) and dividing by a unit capacity.
Question 36Question →

An HVAC technician is installing a straight run of ventilation ductwork that must be exactly 44 yards and 22 feet long. The ducting material comes in standard pre-cut sections that are exactly 2020 inches long. The technician connects these sections end-to-end. Once the connected sections exceed the required length, the excess material is cut off from the final section so the ductwork matches the exact required length. How many inches of material will be cut off and discarded from the final section?

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Answer: 12

Answer

12 inches
First, convert the total required length into inches. Since 11 yard equals 33 feet, 44 yards is 1212 feet. Adding the extra 22 feet gives a total of 1414 feet. Because 11 foot equals 1212 inches, 1414 feet is 168168 inches. Each standard duct section is 2020 inches long. Dividing 168168 by 2020 gives 88 with a remainder of 88 (or 8.48.4), meaning 88 full sections provide only 160160 inches, which is not enough. A 9th9^{\text{th}} section is needed. The total length of 99 uncut sections is 180180 inches. To find the amount discarded, subtract the required length from the total material length: 180−168=12180 - 168 = 12 inches.

Step-by-Step Solution

1
Convert the required measurement from yards and feet into a single unit of inches.
168 inches
Standardizing the units makes it possible to compare the required length directly with the 20-inch section length.
2
Determine the number of 20-inch sections needed by dividing the total required length by the length of one section.
8.4 sections, which rounds up to 9 sections.
The technician must use whole sections and cut the final one, so we must round up to the next whole number.
3
Calculate the total length of the 9 full sections before any cutting.
180 inches
This represents the total raw material used before the final piece is trimmed to fit.
4
Subtract the exact required length from the total raw material length.
12 inches
The difference between the total material length and the required length is the excess that must be cut off and discarded.

Key Concept

US Customary Linear Measurements
Question 37Question →

A diner has 44 gallons of buttermilk in its refrigerator. The kitchen staff uses 22 pints of buttermilk for each large batch of pancake batter. How many large batches of batter can the kitchen prepare?

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Answer: 1616

Answer

1616 batches
First, convert the total volume from gallons to pints. Knowing that 11 gallon equals 44 quarts and 11 quart equals 22 pints, there are 88 pints in one gallon. Multiplying the 44 gallons by 88 gives 3232 pints in total. Then, divide the 3232 available pints by the 22 pints required for each batch to determine that exactly 1616 batches can be prepared.

Step-by-Step Solution

1
Convert the total buttermilk volume from gallons to pints.
4×8=324 \times 8 = 32 pints
To match the unit of measurement required for each batch of batter, knowing that there are 8 pints in a standard gallon (4 quarts per gallon × 2 pints per quart).
2
Divide the total pints by the number of pints used per batch.
32÷2=1632 \div 2 = 16 batches
To find exactly how many full batches can be made from the total available volume.

Key Concept

Converting US customary capacity units and applying unit rates.
Question 38Question →

A food service manager is organizing supplies based on capacity. Arrange the following containers of cooking oil in order from the smallest volume to the largest volume.

Drag items to arrange them in the correct order

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Answer

The correct sequence from smallest to largest is: the 1010 fluid ounce bottle, the 22 cup jar, the 22 quart pitcher, and the 11 gallon jug.
The correct order is determined by converting all container measurements to a single standard unit, such as fluid ounces. The bottle (1010 fluid ounces) is the smallest. Next is the jar (22 cups), which equals 1616 fluid ounces. Then comes the pitcher (22 quarts), which is 6464 fluid ounces. Finally, the bulk jug (11 gallon) is the largest at 128128 fluid ounces.

Step-by-Step Solution

1
Identify a common unit of measurement to compare all the containers.
Fluid ounces is the smallest and most direct base unit to use for comparison.
Converting all volumes to fluid ounces allows for an accurate numerical comparison of capacities.
2
Evaluate the capacity of the small bottle.
The bottle holds 1010 fluid ounces.
It is already provided in the target base unit.
3
Convert the capacity of the jar (22 cups) into fluid ounces.
2×8=162 \times 8 = 16 fluid ounces.
Standard US capacity conversion states that 11 cup is equal to 88 fluid ounces.
4
Convert the capacity of the pitcher (22 quarts) into fluid ounces.
2×32=642 \times 32 = 64 fluid ounces.
Standard US capacity conversion states that 11 quart is equal to 3232 fluid ounces.
5
Convert the capacity of the bulk jug (11 gallon) into fluid ounces.
11 gallon equals 128128 fluid ounces.
Standard US capacity conversion states that 11 gallon contains exactly 128128 fluid ounces.
6
Order the converted numerical values from smallest to largest.
10<16<64<12810 < 16 < 64 < 128.
This mathematically corresponds to the original sequence of containers: bottle, jar, pitcher, jug.

Key Concept

Converting and comparing standard US customary units of capacity in a real-world context.
Question 39Question →

A stage crew is connecting two sections of metal piping end-to-end to build a vertical pole for a lighting rig. The bottom section is 2122 \frac{1}{2} yards long. The top section is 44 feet 66 inches long. What is the total height of the assembled pole in yards?

Show answer & explanation

Answer: 44

Answer

The total height of the assembled pole is 44 yards.
To find the total height, both measurements must be converted to the same unit. The top section is 44 feet 66 inches, which is exactly 4.54.5 feet. Since there are 33 feet in a yard, dividing 4.54.5 by 33 yields 1.51.5 yards (or 1121 \frac{1}{2} yards). Adding this to the bottom section's length of 2122 \frac{1}{2} yards gives exactly 44 yards.

Step-by-Step Solution

1
Convert the length of the top section from feet and inches to a single unit (feet).
44 feet 66 inches equals 4.54.5 feet (since 66 inches is half of a foot).
It is necessary to express the length in a uniform unit before converting it to yards.
2
Convert the top section's length from feet to yards.
4.54.5 feet divided by 33 feet per yard equals 1.51.5 yards (or 1121 \frac{1}{2} yards).
The final requested answer is in yards, so both sections must be expressed in this unit.
3
Add the lengths of both sections in yards.
212 yards+112 yards=4 yards2 \frac{1}{2} \text{ yards} + 1 \frac{1}{2} \text{ yards} = 4 \text{ yards}.
Connecting the pipes end-to-end means their total combined height is the sum of their individual lengths.

Key Concept

Converting mixed linear measurements (feet and inches) to yards and adding fractional quantities.

Alternative Method

Convert all measurements to inches first. The bottom section is 2122 \frac{1}{2} yards, which is 2.5×36=902.5 \times 36 = 90 inches. The top section is 44 feet 66 inches, which is 48+6=5448 + 6 = 54 inches. Add them together to get 144144 inches. Finally, divide by 3636 inches per yard to get exactly 44 yards.
Estimated Time:1m 0s
Question 40Question →

A civil engineer is evaluating four proposed segments for a new neighborhood walking trail. To properly allocate paving materials, the segments must be organized by length. Arrange the following trail segments in order from shortest to longest.

Drag items to arrange them in the correct order

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Answer

The correct order from shortest to longest is: Birch Path, Cedar Path, Elm Path, Oak Path.
By converting all distances to a common unit (feet), we find that Birch Path is 325 feet, Cedar Path is 326 feet, Elm Path is 330 feet, and Oak Path is 331.5 feet. Arranging these numbers from smallest to largest yields the correct sequence.

Step-by-Step Solution

1
Select a common unit of measurement to compare all segments.
Feet is the most practical common unit for these values.
Comparing different units (inches, yards, miles) directly leads to errors.
2
Convert Birch Path from inches to feet.
3,900÷12=3253,900 \div 12 = 325 feet.
There are 1212 inches in 11 foot.
3
Convert Cedar Path from yards and feet to total feet.
108×3=324108 \times 3 = 324 feet. Adding the remaining 22 feet gives 326326 feet.
There are 33 feet in 11 yard.
4
Convert Elm Path from miles to feet.
5,280×116=3305,280 \times \frac{1}{16} = 330 feet.
There are 5,2805,280 feet in 11 mile.
5
Convert Oak Path from yards to feet.
110.5×3=331.5110.5 \times 3 = 331.5 feet.
There are 33 feet in 11 yard, and 11012110 \frac{1}{2} can be written as 110.5110.5.
6
Order the converted values from smallest to largest.
325325 feet < 326326 feet < 330330 feet < 331.5331.5 feet.
The question asks for the order from shortest to longest.

Key Concept

Converting between US Customary linear measurements (inches, feet, yards, miles) to establish a common unit for comparison.
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